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MAGNETIC RESONANCE AND THE PROBLEM OF THE DEFINITION OF ANTIFERROELECTRICITY
H. Gränicher
To cite this version:
H. Gränicher. MAGNETIC RESONANCE AND THE PROBLEM OF THE DEFINITION OF ANTIFERROELECTRICITY. Journal de Physique Colloques, 1972, 33 (C2), pp.C2-187-C2-188.
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JOURNAL DE PHYSIQUE Colloque C2, supplkment au no 4, Tome 33, Avril 1972, page C2-187
MAGNETIC RESONANCE AND THE PROBLEM OF THE DEFINITION OF ANTIFERROELECTRICITY
Laboratory of Solid State Physics, ETHZ, CH-8049 Ziirich, Switzerland
R6sum6. - Contraire au cas des ferroiJectriques, I'attribution (( antiferroklectrique )) nkcessite des donnks sur le cristal qui s'etendent au-dela du niveau macroscopique (groupe ponctuel). Comme illustre par l'exemple du periodate d'ammonium ces informations detaillkes peuvent Stre obtenues par I'btude des interactions quadripolaires. On souligne que la definition de I'antiferro6lectricit6 doit Stre restreinte aux cristaux, dans lesquels des interactions electriques sont essentielles pour le mbca- nisme qui provoque la transition de phase.
Abstract. - In contrast to the case of ferroelectrics the assignment of antiferroelectricity pre- supposes information on the crystal which goes beyond the macroscopic (point group symmetry) level. Illustrated by the example of ammonium periodate these fulldata may be obtained by the study of nuclear quadrupole interactions. It is emphasised that the definition of antiferroelectricity has to be restricted to crystals, in which electric interactions are essential for the driving mechanism of the phase transition.
1. Introduction. - It is possible to identify a crystal as ferroelectric by the phenomenological (macroscopic) observation of a switchable or - more generally speaking - of a reorientable spontaneous polarization alone. By now it is well established that the knowledge of the point symmetry of the non- ferroelectric high temperature phase (also called parent or initial phase) and of the orientation of the spon- taneous polarization is sufficient to determine the point symmetry of the ferroelectric phase (see review by Shuvalov [I]). The same macroscopic data are adequate for the assignment of the symmetry of the ((soft )>
mode responsible for the ferroelectric transition, as shown recently by Lavrencic and Blinc [2]. Therefore, experiments which yield information at the atomistic (space group) level are not a necessity for assigning a crystal as ferroelectric. However, e. g. the investigation of the phonon dispersion is an important alternative in cases where no dielectric studies are possible as treated by Steigmeier earlier in this meeting [3].
The situation is quite different in antiferroelectricity.
Kittel [4] who introduced the concept by analogy to antiferromagnetism postulated the existence of sponta- neously polarized lines of ions with neighbouring lines polarized in antiparallel direction, so that no macro- scopic spontaneous polarization of the crystal results.
It is generally accepted that any definition of antiferro- electricity includes the requirement of an antipolar crystal structure. As already Kanzig [ 5 ] had shown, an antipolar structure need not have a multiple elemen- tary cell as compared to the parent phase, but no such cases seem to be known. Apart from this special situation where parent and antiferroelectric phase are possible in the same space group, the translation symmetry of the crystal changes at the antiferro-
electric transition point. As a consequence, the know- ledge of the point group and of purely macroscopic properties of the crystal is not sufficient to assign antiferroelectricity to a crystal phase.
2. Critical comment. - Before we start to discuss the virtues of nuclear quadrupole resonance investiga- tions as means of obtaining information at the atomis- tic (space group) level, we have to point out that there is some controversy about the definition of anti- ferroelectricity. If the antipolar structure is the only prerequisite, then many crystals such as SrTiO, (below 105 OK) qualify as antiferroelectric. These are cases with practically no anomaly of the dielectric behaviour at the phase transition. As the driving mechanism is a cc soft )) mode of rotational character, there is no essential interaction to electric fields (see discussion by Granicher and Miiller [6]). The present author had proposed in 1957 [7] that the use of the term antiferroelectric should be << restricted to cases, where the interaction is essentially of the same nature as in ferroelectrics )). Such an amendment to the defi- nition of the antiferroelectric state has been formulated by Jona and Shirane [8] in terms of thermodynamics.
They call an antipolar crystal antiferroelectric if its free energy is comparable to that of a polar crystal. Today this is best understood in terms of Cochran's theory of distortive phase transitions. Kittel's thermodynamic theory can be expressed by two lattice vibration modes with a strong temperature dependence of their fre- quencies (Cochran and Zia [9] and Zein et al. [lo]).
Experimental evidence for a ferro- and an antiferro- electric mode in PbZrO, has been given recently by Samara [Ill.
Without giving further details here, we emphasize
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1972263
that the definition of antiferroelectricity in the restrict- ed sense is adequate to the character of the mechanism driving the crystal into the antiferroelectric state.
3. The application of spin resonance to antiferro- electrics. - In antiferromagnetism the magnetic scattering of neutrons offers a unique tool to reveal the antipolar sublattice magnetization. Unfortunately there is no electric analogue to this method of investigation.
Therefore, we turn to the question what evidence may be derived from spin resonance techniques. Here too, the magnetic case is easier to solve. A particularly straightforward and illuminating example is the study of Poulis and Hardeman [I21 on CuCl, .2 H,O. This crystal becomes antiferromagnetic below TN = 4.37 OK The protons are subject to the external magnetic field H,, plus the local field produced by the antiparallel copper ion sublattice magnetizations. By taking a rotation pattern of the proton resonance lines, the field contributions due to the sublattices become directly apparent.
In the electric analogue it is possible to sense the electric field not directly but its gradient at the sites of nuclei with electric quadrupole moments. This looks like a disadvantage at first sight, but in suitable materials a wealth of information can be derived from NQR investigations. It is basic that the symmetry properties of the electric field gradient (E. F. G.)
tensor are determined by the point symmetry at the site of the nuclei under study. In addition to sites which are related by the crystal symmetry (physically equiva- lent sites), there may be chemically inequivalent nuclear sites which e. g. show up when the crystal is cooled through the transition temperature.
Shimomura [13] argued that the Laue group of a crystal may be determined from the number of orienta- tions of equivalent E. F. G . tensors. But his conclusion that the analysis of the N. Q. interaction does not offer more information than the Laue technique in X-ray scattering is not correct. An interesting example is the investigation of the so called (< antiferroelectric )) phase of ammonium periodate (NH,),H,IO, [14]. As the chemical formula and the room temperature structure of this material were known, the low temperature phase could be derived from 112' resonance data in great details. An ambiguity between two allowed space groups remained. But similar studies on deuterated crystals will enable to decide between the two groups.
The structure model obtained may be checked by a consistent calculation of all the observed E. F. G.
tensor components.
All the information described above is derived from the resonance spectra. An additional and powerful source of information is the study of the temperature dependence of the spin-lattice relaxation time T I as presented at this meeting by A. Rigamonti 1151.
References [I] SHWALOV (L. A.), J. Phys. Soc. Japan, 1970, 28,
suppl. 38-51.
[2] LAVRENCIC (B.) and BLINC (R.), Phys. Stat. Solidi (B), 1972, 49, K 119.
[3] STEIGMEIER (E. F.), these proceedings.
[4] KITTEL (C.), Phys. Rev., 1951, 82,729-732.
151 KANZIG (W.), (( Ferroelectric~ and Antiferroelectrics )) in (( Solid State Physics )I, F. Seitz and D. Turn- bull (Editors), Vol. 4, 1957.
[6] GRXNICHER (H.) and MULLER (K. A.), Mat. Res.
Bulletin, 1971,6,977-987.
[7] GRANICHER (H.), NUOVO Cimento, Suppl., 1957,6,1220- 1223.
[8] JONA (F.), SHIRANE (G.), (( Ferroelectric Crystals D,
Pergamon Press, Oxford, 1962.
[9] COCHRAN (W.) and ZIA (A.), Phys. Stat. Sol., 1968, 25,273-283.
[lo] ZEIN (N. E.), ZINENKO (V. I.) and SHNEIDER (V. E.), Soviet Physics. Solid State, 1971, 12, 1858-1863.
[Ill SAMARA (G. A.), Phys. Rev., 1970, B1, 3777-3786.
[12] POULIS (N. J.) and HARDEMAN (G. E. G.), Physica, 1954, 20, 7-13.
[13] SHIMOMURA (K.), J. Phys. Soc. Japan, 1957,12,652.
[I41 KIND (R.), Phys. Konden. Materie, 1971, 13, 217-245.
[IS] BONERA (G.), BORSA (F.) and RIGAMONTI (A.), these proceedings.
